Toss bombing apparatus



Sept. 10, 1957 H. s. MORTON TOSS BOMBING APPARATUS 5 Sheets-Sheet 1Filed June 1, 1944 gwuc/wbom Hurnld IE]- M ar a an T "known L w ouuhavubw ukw MCKELV. E 3% x fi wmm Sept. 10, 1957 H. s. MORTON 2,805,601

TOSS BOMBING APPARATUS Filed June 1, 1944 3 Sheets-Sheet 2 gnaw bowHurnlpl E1- Murctlii @294 a flmmm 4% Sept. 10, 1957 H. s. MORTON TOSSBOMBING APPARATUS 3 Sheets-Sheet 3 Filed June 1, 1944 A 2 WWgwuc/vvto'r/ l-luruld E1- Mar-"c an 2,805,60l Patented Sept. 10, 1957 12,805,601 TOSS BOMBING APPARATUS Harold S. Morton, Takoma Park, Md.,assignor to the United States of America as represented by the Sec=retary of War Application June 1, 1944, Serial No. 538,311 Claims. (Cl.89-15) (Granted under Title 35, U. S. Code (1952), sec. 266) Theinvention described herein may be manufactured and used by or for theGovernment for governmental purposes without the payment to me of anyroyalty thereon.

This invention relates to a method of bombing by aircraft andparticularly to a method of plane-to-plane bombing.

Close formations of heavily armed bombing planes have recently beensignally successful in their ability to perform their mission in spiteof heavy attacks by enemy planes. At the same time such formations areable to inflict severe losses on the attacking planes. There istherefore a need for technique which will damage :or destroy theindividual planes in such bomber formations, or force the dispersion ofthe formation so that pursuit planes can deal with the bombing planesindividually, without exposing the attacking plane to the concentratedfire of the formation at short ranges.

The bombing of such a formation by an attacking plane has beenheretofore suggested. The suggested method however generally involvedthe attacking plane flying parallel to and at a greater altitude thanthe bomber formation, hence requiring a vertical fall of the bombs ofthe attacking plane. Such a method when employing bombs equipped withcontact fuses cannot be successful against an alert enemy for thefollowing reasons: a. When the bomb is released from a safe distanceabove the enemy bomber formation, the time of fall of the bomb permitstime enough for evasion by the bomber formation. For example, neglectingair resistance, in the first second the bomb falls only sixteen feet, inthe first two seconds, sixty-four feet, etc. so that if the attackingplane stays at a relatively safe distance of 3000 feet above the bomberformation, approximately eleven seconds are required for the bomb tofall to the target. b. With contact fuse bombs, a direct hit on one ofthe bombersin the formation is necessary and of course is extremelydiflicult to achieve. c. The determination of the proper point ofrelease by systems of sighting which must take into considerationrelative velocity, range, and difference of altitude tends to be a verydifficult process requiring complicated apparatus.

Accordingly, it is an object of this invention to provide an improvedmethod of bombing by plane, particularly effective against flyingtargets but equally applicable to targets on land or water.

A particular object of this invention is to provide apparatus forcarrying out the bombing method disclosed herein.

The specific nature of the invention as well as other objects andadvantages thereof will clearly appear from a description of a preferredembodiment as shown in the accompanying drawings in which:

Fig. l is a schematic diagram showing the path of a projectile releasedfrom an attacking plane flying a horizontal course after such plane haspulled upwardly with an acceleration of 2g or greater and released aprojectile at the point R.

Fig. 2 is a schematic diagram showing an attacking plane flying on acollision course with respect to a target plane, illustrating the lineof sight between the attacking plane and target plane at successive timeintervals t1, 12 etc.

Fig. 3is a view similar to Fig. 2 but showing the path of the projectileafter the release of such projectile at the point R with coordinatesbased on the horizontal.

Fig. 4 is an enlarged diagrammatic view of a portion of Fig. 3. i

.Fig. 5 is likewise a diagrammatic view of a portion of 1 Fig. 3.

Fig. 6 is a view similar to Fig. 4 but with the horizontal coordinateaxis parallel to the line of flight of the target plane.

Fig. 7 is a diagrammatic view showing the last plane in theflight'nearest to the attacking plane utilized for sighting purposeswhen releasing the bomb on a steep dive approach. The path of suchreleased bomb is also shown.

Fig. 8 is a diagrammatic view showing a generalized condition of anattacking plane flying a collision course at A and then pulling up torelease the projectile at a point B and also showing the projected pathof such projectile after release at point B.

Fig. 9 shows diagrammatically a simple form of integrating delayedrelease mechanism.

Fig. 10 is an elevational sectional view of an airplane carrying thetoss bombing mechanism of this invention.

In the bombing method comprising the present invention, the pilot of thebombing plane flies, at uniform velocity, on a straight line coursewhich, if continued indefinitely, would cause him to collide with thetarget. While still a safe distance from the target, he determines, inany conventional manner, how far away he is in terms of time from thetarget. Knowing this information, the bombing plane is given a propervertically upward acceleration for a long enough period of time toinsure that the velocity of the bomb, when the latter is releasedshortly thereafter, will be such as to cause the bomb to cross theoriginal line of flight of the bombing plane close enough to thetheoretical collision point of the planes to insure proper functioningof the fuze on the target, assuming that the latter, i-f moving, has notchanged its speed or direction of flight. Acceleration integrating meansis provided, according to the invention, for delaying the release of thebomb during the acceleration of the plane until the proper bomb velocityhas been reached to accomplish the desired result.

My invention may be used with any bomb carrying airplane. As suggestedin Fig. 10, the bomb 30 is normally carried along the belly of theairplane 31 and is detachably connected thereto by fasteners 32. Thefasteners 32 operate to release the bomb in response to functiming ofthe bomb release mechanism 33. Bomb release mechanism 33 is in turnresponsive to the acceleration integrator 34. In the palticularintegrator, shown in detail in Fig. 9, a predetermined rotationaldisplacement of shaft 22 depends upon an integration of verticalaccelerations of the airplane over a period of time to give thenecessary vertical component of the velocity to the airplane and itsbomb. Upon attainment of this velocity the bomb is released and itsflight to a target is assured. Angle of flight with respect to theactual horizontal is indicated by a conventional artificial horizon 36.

It will be apparent that the present method can be utilized in bombingstationary or moving targets on land or sea or in the air. In the caseof a stationary target, the line of flight of the bombing plane will bea straight line to the target. For a target moving in a straight line atuniform velocity, which will be the usual case, the line of flight ofthe bombing plane and the course of the target will be straight linesintersecting at the collision point.

The method of bombing in accordance with this invention is particularlyeffective with bombs equipped with proximity fuses. The specific natureof such fuses forms no part. of this invention and such fuses may be anyof several known constructions. In general such fuses have an armingtime on the order of several seconds which permits the plane releasingthe bomb to get sufficiently faraway from the bomb after it isreleased'that'the releasing plane will not accomplish the detonation ofthe bomb, Such fuses are generally effective to detonate the bomb'whenthey approach within one hundred fifty feet or less of thetarget object,which. of course is well within the effective destruction range of a 500pound or larger bomb. i

The technique of flying a collision course toward the target applies notonly to direct head-on attack from the same level and directly in frontof the target, as where the target is an enemy airplane, but also to approaches at' an angle, in which the bombing plane and the target havestraight line intersecting courses, and *to approaches from above, in adive bombing attack or l,

even from a lower level in a climbing approach; The method constitutingthis invention is most clearly understood when applied to conditionswhere the attacking plane is flown straight into the face of oncomingenemy planes, at the same level and flying directly down means in theline of sight of the attacking plane will 7 serve the same purpose. Uponreaching a predetermined range from the approaching enemy, which rangewill be shown to be not very critical, the attacking plane pulls upsharply and-by means of apparatus to be described, releases his bombslightly after beginning the pull-up. The eflfect of this maneuver is togive the bomb a slight upward toss whereby the bomb first rises slightlyabove the line of flight of the approaching enemy plane, reaches zeroupward velocity and then falls below such line of flight in accordancewith the gravity forces. operative on the bomb. However, the bomb has ahorizontal velocity of approach to the enemy plane equal to the sum ofthe velocities of the attacking and target planes.

. The desirability of this method will be clearly evident from thefollowing table. In this table there has been calculated for pull-upaccelerations of the attacking plane ranging from 2% g to 4 /2 g thenecessary time delay 'in release of the bomb from the beginning of theupward acceleration to produce upward velocities of the bomb of 64, 72,and 80 feet per second. The vertical positions of the bomb with respectto the original line of flight of the attacking plane is also tabulatedshowing the height of the bomb at release, the maximum height attained,and the height at 4, 5, and 6 seconds respectively after release withrespect to the horizontal path of the target.

From above table, it will be apparent that the released bomb will liewithin a hundred and fifty feet vertically of the line of flight of theenemy' plane formation for at least five seconds after release of thebomb, and with the eighty foot-seconds upward velocity at release, forsix full seconds. As has'already' been mentioned the bomb is approachingthe target'plane with a horizontal velocity equal to the sum of thevelocities of the attacking and target planes. If each plane. is assumedto be flying at the rate of three hundred miles per hour, the rate ofapproach is 880 feet per second. Neglecting the retarding etfect of airfriction (which in the case of heavy bombs. has been found to reduce therange less than forty feet at 300 miles per hours), a bomb may bereleased 4400 feet horizontally from the target and reach the newhorizontal positionof the target infive seconds. In this example, theattacking plane thus could release its bomb elevent times 'as far away'from the target in accordance with this method than an attacking planerelying solely on the vertical fall of the b01111). V r

The limiting factor in determining how close the attacking plane canapproachthe target before releasing a bomb with a proximity fuse 'is thetime necessary for theattacking plane to get a reasonably safe distanceaway from its own bomb before it becomes armed and operates on the.target. As has been shown, it is not suflicient for an attacking planeto rely solely on gravity to put distance between it and the bomb.However, in accordance' with this invention the attacking planepulls'upward away from the bomb with an acceleration of at least 2 /2 g.The following table has been Eomputed to show the separation between theattacking plane and the bomb if the attacking plane pulls sharply upwardimmediately after release of the bomb.

TABLE B Separation from. released bomb 5 The foregoing table wouldindicate that an arming delay time on the order of four seconds willprovide. ample safety for the attacking plane if the'pilot pulls upwardwith an acceleration of at least 2 /z' g. If the pilot is willing topull up with a higher? acceleration,

the arming time may be still further reduced. 1

Referring to Tables A and B with the specific exam- TABLE A TotalAcceleration 2% g 3 g 3% a 4 g 4% a a Time to Release 1.33 1.0 0.8 0.67O. 57

- aximum eig Upward Venom Height 4 sec. after Releas 43 32 2e 22 11s 9-Height 5 see. after Release- -a7 -48 -54 -58 -e2 Height 6 see. afterRelease .do -149 --160 166 170 174' Time to Release .seconds 1. 5 1.120. 9 0.76 0. 64 V I I et. 54 40 32 27 2g 72lsec. Upward Velocity 2 g g;2 r at Release. 1 1 13 -89 ,1o5 -111 116 --12a 1. 67 1.25 1.0 0. 0. 7167 50 4O 33 28 80lsee. Upward Velocity g 167 150 133 128 at ReleaseHeight 4 see. after Releas 131 114 104 97 92 Height 5 see. afterRelease- .d 67 5O 4O 33 28 Height 6 sec'. after Release do -29 46 56 -6368 Height 7 see. after Release do 157 -174 -J .84 191 -198 ple of bothattacking and flying planes flying at 300 miles per hour, the advantagesof bombing methods in accordance with this invention are apparent. Ifthe bomb fuse is set to produce a four-second arming time delay and thepilot pulls up with an acceleration of from 2 to 4 /2 g, releasing thebomb with an upward velocity of 72 feet per second, then as illustratedin Fig. 1, his bomb may be released at a range varying from 3520 feet to5280 feet from the target and the bomb will nevertheless be armed andwithin 150 feet vertically of the target when it reaches the samehorizontal position as the target. Furthermore, the attacking plane willbe safely out of range of harm both from its own bomb and the fire ofthe target plane. Since the proximity fuse will cause detonation of thebomb at an approach of 150 feet or less to the target, the probabilityof damage to the attacking plane, and particularly to a formation ofattacking planes, is very high.

The enemy must take sharp evasive action within a very short time toavoid the effective area of the bomb. It is obviously an advantage forthe attacking plane to keep the time between the release of the bomb andits reaching the vicinity of the target as low as is consistent with thesafety of the attacking plane. If the time is kept low, a formation willnot have suflicient time to make any efiective change of pace ordirection after the bomb is released. The enemy may start to turn assoon as he sees any planes making a frontal approach. This can readilybe defeated by flying several attacking planes abreast of each other, sothat no matter which way the enemy plane turns, some one attacking planeis in front of him. Movements of the enemy up or down can be matched bythe attacker and even if the enemy at the last moment takes a course atthe last line between him and the enemy plane, the latter can aim, notat the enemy plane itself, but at the imaginary spot where the enemyplane will be if it continues its new course until the bomb meets it.

Following is a mathematical analysis of the uniform level-head-on attackmethod. Referring to Fig. 1 the attacking plane A is flying horizontallymaintaining a uniform level-head-on approach to enemy plane E. Theattacking plane A is equipped with a delayed release mechanism on itsbomb rack, which will be described later, to delay the release of thebomb until a predetermined upward vertical velocity is attained by theattacking plane. At point B the pilot presses the release trigger andimmediately pulls up sharply with an acceleration of 2 g or more. Thedelayed release mechanism holds on to the bomb until it reaches point R,at which point it has a vertical velocity v and has been lifted adistance L above the original line of flight.

At the time of release the bomb has the same speed as the plane in adirection tangent to the line of flight. This velocity V is resolvedinto its vertical component v and its horizontal component V11.

In precise calculations of the trajectory consideration must be given tothe fact that Vh is one or two percent less than V. For thispresentation secondary effects of minor character will be disregarded,while a general conception of flight characteristics is developed.

Let

then

pulling up.

A mechanical delayed release mechanism will be later described whichwill in effect integrate the above relationship and hold up the releaseuntil a predetermined upwardly velocity is reached, regardless ofwhether the pull-up be gentle or abrupt.

Let 0 be the origin of a system of rectangular coordinates; and lett=time in seconds after release at point R whose coordinates are x=o y=LProperly chosen values of v will cause the bomb trajectory to cross theoriginal line of flight (and line of sight) any desired number ofseconds after release, as shown at x .(Fig. 1). Anywhere between pointsC and D is close enough to the line of flight to be effective, so therecan be considerable error in determination of range or velocity ofapproach without causing a miss, because of the flatness of thetrajectory.

For example a trajectory will be calculated for V='440/sec. v='/sec.a=96'/sec./sec. from Equation 3 above L=50 feet.

TABLE C [Time (1!) seconds] z 1,760 1,980 2,200 2, 420 2, 640 2, 8603,080 11 114 86 50 0 -4a 10B 174 The crossing point is just past 5 /2seconds or 2420 feet after release, but the trajectory is at no pointmore than feet off the line of flight until just before 7 seconds haselapsed.

If the enemy is approaching at 440/ sec. and assuming an arming time of4 seconds, the distance between the two planes at time of release mightvary from about 3520' to about 6000 feet, a difference of nearly /2mile, without causing a miss.

The principles of this invention are equally applicable to all otherapproach situations to both moving and stationary targets in addition tothe uniform level-head-on approach already discussed. concepts of thisinvention are involved in the angular approach. The method of theinvention may be stated in the following general terms. Assuming thatthe enemy plane has been sighted and is moving in a fixed course at auniform velocity, the attacking plane need only assume a flightdirection and velocity whether level flight, climbing, or diving whichif maintained uniformly will intersect the enemy plane. In other wordsthe attacking plane flies a collision course with respect to the enemyplane. The attacking plane now may consider itself as a fixed referencepoint of a system of coordinates. The target then appears as an objectapproaching the fixed reference point at a uniform velocity along astraight line. To the pilot of the attacking plane, it appears that theapproaching object will strike him if he does not move out of the way.Accordingly, by apparatus to be described, the pilot ascertains theexact length of time existing prior to the impending collision. He thenmoves 01f his course to avoid the collision and thereby moves In factthe most general.

' right angles to the collision course.

away. from the fixed reference point. As he does so, he tosses. thebombvertically upward with just sufiicient velocity. that it .will rise,stop, and fall back to the fixed reference point in exactly the samenumber of seconds that will be taken by the target to reach the samepoint.

With this concept of the method of bombing in accordance with thisinvention, it is thereforeimmaterial whether the path of the attackingplane is horizontal, diving, orclimbing so long as the attacking planeis fast enough to fly on a course which will eventually collide V withthe target.

The attacking plane may readily fly on the necessary collision coursewithout requiring special instruments or computing mechanisms. Referringto Fig. 2, an attacking plane at A observes, an enemy plane at E. Whenfirst observed the enemy plane in general has an apparent angular motionabout the attacking plane. The attacking plane is turned in'such a wayas to head off the apparent movement of the enemy which is accomplishedby getting on'a'c'ourse at B such that the line of sight A enemycontinues to maintain the same absolute orientation with respect to theattacker, the two must inevitably collide, if the courses are continued.

The principle is the same as that habitually used in navigating to reacha certain destination in a cross-wind. The plane does not point towardits destination at all, butit does maintain a constant orientation whichultimately brings it'directly to the destination. The same principleapplies to, a plane approaching another, not directly head-on, but at anangle from the side. For each condition of relative speeds and angle oforientation, the attacking plane can swing to a line of flight whichconstantly'maintains the other plane in the same absolute orientation,just as long as both continue to fly a straightline, uniform speedcourse. It makes no difference whether the geometric plane containingthe two intersecting flight lines is horizontal, vertical or oblique.

Under any of these conditions, when the attacking plane on its collisioncourse is considered as the reference point, the target will appear tobe approaching along a straightline at a uniform velocity. There ishowever, a marked difference in the direction of toss of the bombobtained by merely pulling up, according towhether the attacking planeis flying level or at an angle with respect 'to the gravity'axis. Anattacking plane flying level and then pulling up off the collisioncourse imparts only a vertical upward velocity of the bombwith respectto the reference point. 'When the attacking plane is diving ordiagonally climbing, a bombtossed by pull up will not have a resultantvelocity vertically upward but will be directed at Under suchconditions, it is more difficult to toss the bomb with only a resultantvertical upward velocity with respect to the reference point. It ishowever possible to obtain such a resultant velocity in a diving planeby a simultaneous change in direction of the plane, such as by pullingout of the dive, and simultaneously reducing the speed of the dive bythrottling the motor and/or lowering the wing flaps. Proper coordinationbetween the rate of pullup and rate of reduction of speed will give aresultant toss which is straight up, relative to the fixed referencepoint. If a toss of this type is accomplished then the relationshipscomputed in Tables A and B are still accurate and hence the sameadvantages are obtained independent of direction of approach to target.

It will now be demonstrated that only a small, readily compensatederroroccurs in the application of the bombinamet pd 0.1": t sinventiqato an ns a appma o the In the vertically upward toss of the,bomb, the superelevation? causes the resulting evolute' bombtrajectoryto lie above the projected linefof flight for a certain nurnberrofseconds until gravity pulls it backacross thelline. In the tossperpendicular to an angular collision course, two new factors enterinto. the problem: a. The trajectory does not curve back toward theoriginal line of flight of the releasing plane as fast as in the case ofhorizontal flight because only a part of the force of gravity acts as arestoring force in this direction. b. The bomb does not travel abreastof the corresponding positions on the releasing planes collision courseas time goes by; but it accelerates its velocitydue to the component ofgravity and runs further and further ahead of the projected planepositions (which are predicated on constant speed).

Referring to Fig. 3, the family of parallel lines t1, t2, ts, etc., arecalled isochronous lines, and represent the orientation of the targetwith respect to thejattacking plane at various times. (Note: The exactposition of the target on any one of these lines is not known, and hencethe exact time at which the collision-point of the two courses isreached will require instrument determination by apparatus to bedescribed.) It is necessary to examine the parabolic trajectory of thebomb and see Whether, at successive times, :1, t2, t3, etc., it isreasonably close tothe isochronous lines corresponding to the samerespective times.

. It will be noted from Fig.3 that at a time the bomb t4 will reach itsclosest approach to the target plane at a point G before the targetreaches the collision-point on the intersection of the two flight lines,and at a lower level than the corresponding point H on the attackingplanes projected course. This shows that the two new factors discussedunder a and b, above,'produce compensating effects which make itpossible to score hits (or be within fuze radius) over a-considerablerange of time'intervals, in dive-bombing attacks, just as in levelflight attack.

This effect can be investigated mathematically by setting up'equationsfor the parabola and the isochronous lines, in a system of rectangularcoordinates with point 0 (Fig.

3) on the projected path of theattacking plane as the Equations for. theparabolic trajectory of the bomb by application of'well known formulaeare then: V

x=L sin or+vl sin a +Vt cos at T (6) Equations for the family ofisochronous lines:

y=x tan 0n When t and n are bothzero tion of Fig. 3 at any time t, thevalue ofn is represented by GA.

AB=BD tan 0=Vt cos 0: tan 0 Assigning proper algebraic sign to theseveral terms the equation for the isochronous lines becomesz y=x tan0+Vt cos or tan t2-Vt sin or (9) Any given values of t define aparticular point 011 the parabola, and give the equation of a particularline when substituted in the isochronous line formula. It becomes ofinterest to determine the value of y on the isochronous line t for thevalue of X as found on the parabola for t and then to see what thedifierence is between the y point L of the parabola and the y point K ofthe isochronous line. Such difierence is illustrated graphically as theline KL on Fig. 5 which is a view of a portion of Fig. 3.

Substitute in the formula for the isochronous lines, the value of x forthe parabola as follows:

isochrone: y=x tan 0+Vt cos a tan -Vt sin a x of parabola: x=L sin u+vtsin a-f-Vl cos a (6) Substitution: i

y=--L sin oz tan 9-vt sin a tan 9-- V2 cos a tan 0+Vt cos 0c tan 0-4 1sin a =L sin or tan 0vt sine tan 0-Vt sin a Subtract this value of yfrom the value of y for the parabola which is:

in order to get the value of KL- the difierence in values of y forvarious values of t. The closest approach to the path of target is theline LM and is found by multiplying KL by cos 0.

KL=L cos 06+Vt cos oc-Vt sin u- /zgr L sin a tan 0+vt sin a tan 0-l-Vtsin a KL=(L+vt) (cos oc-I-Sifl a tan i9) /2gt (10) The relationshipsbetween or and 0 obviously depend on the relative velocities of the twoplanes. Referring to Fig. 6 where the x coordinate axis is takenparallel to the flight of the target plane B:

Let

Sin 0:

tan 0= (11) cos ark- In order to adjust the constants in the trajectoryequations to the proper values, let the y=ditferences, or KL of Fig. 5,equal zero at the value of t at which greatest accuracy is desired.

KL=(L+vt) (cos ut+sin a tan 0)- /2gt 12 =0(L+vt) (cos a+sin a tan 6l)=/2g1:

Now substitute value of tan 0 in terms of a derived in (11) aboveSolving for Sin 0:

t (1 cos a+ cos cplranging from one to zero.

In this table the time from bomb release to reaching of collision pointhas been selected as six seconds and a net pull out acceleration of 3gshas been assumed.

TABLE D [Values of 11.]

Indications of the above table, drawn up for maximum accuracy sixseconds after release of the bomb are that when the velocities of bothplanes are equal, or

V 1 the angle of dive at has no effect on the required velocity of thebomb produced by the delayed release mechanism; but when the targetplane is at a lesser velocity, the perpendicular component of bombvelocity v should be reduced as the angle of dive increases. The lowerthe target velocity, the greater is the reduction in velocity v withincreased angle of dive. This correction to the delayed releasemechanism obviously could be made manually by the pilot of the attackingplane in anticipation of the probable relative speeds of the targetplane and the attacking plane.

The following numerical example is presented to illustrate how close thebomb will come to the isochronous lines, each of which is intersected bythe target plane, at various times from four to eight seconds after itsrelease when the value of v corresponds to that shown in the precedingtable.

The perpendicular distance between the bomb and any isochronous line isof course LM of Fig. 5. Let plane and target velocities be equal or Letat equal 40; then from Table D v=87 feet per second and L=54 feet.

sin a Substituting in Equation '10 sin a KL-(L+Ut)(COS a+m)}gt =Llvtygtand I, W.

MK=(L+vt-%gt cos a 14) From Equation 14 the following. table has beencom puted: V

.11 TABLE E"' Distance between bomb and isochronous lines to-targetplane as function of time [t (seconds)] 44 5 5% 66% vw's LM (feet).. 137115 85 45 0 64 114 181 257 It will be understood that when a steepdive-bombing attack is made with an approach from a quartering posiation instead of directly in front, the over-run of the bomb discussedabove will cause it to carry beyond the course of the enemy plane. Itwill tend to make the hit on the second or third plane on the flank ofthe formation opposite the attacker, unless some corrective measures aretaken. This phenomenon resembles the effect of angle of lag oncross-wind bombing, and will only eflect this technique on angularapproaches across the enemys course.

Note that this effect is not present if a cross-course approach is madeat the same level; and it is not significant at moderate angles of dive.7 It only becomes noticeable in steep dives considerably to one side ofa head-on ap proach. In order to evaluate the importance of this effect,an analysis will be made of the over reach by which the bomb trajectorylies ahead of the projected line of the dive-bombers course at varioustimes after release of the bomb.

The projected line of flight of the plane (Fig. 6) is at an angle atbelow the x-axis and starts from the origin. Its equation may bewritten:

y=x tan a or x=y cot a (15) Substitute for y the value for the parabolafrom Equation y=L cos a+t1t cos aVt sin 01%;]? (7) Then, a2: L cos a cota-Ui cos a cot (1+ Vt sin a cot. a-Hgt cot a cos 0: cos a 2 :v-- L sin avt sin a cos Obi- 19 cot a Subtract this from the value of x for theparabola from Equation 6 to obtain the-horizontal over reachz x=Lsina+vt sin oH-Vi boso (6) Over reach= The preceding table illustrates howfar thebomb over reaches horizontally the isochronous lines to the enemyplane. Thus the enemy plane is always short of .its: collision-point?with the course of the bombing plane, because, in the oblique attack.the over-reac of the bomb, and its accelerated downward speed cause itto meet thetarget sooner than the attacking plane would reach thecollision-poin and sooner than the enemy 12 plane would reach theattacking planes coursel- There-v fore, in the oblique approach,dive-bombing attack, the bomb falls beyond the collision-point inprolongation of the attacking planes course, and the enemy plane isshort of reaching the theoretical collision-point. It is noted from thetable in the preceding paragraph that at six seconds the distance ofover-reach is 206 feet which is just a little more than fuze ranges. Theamount by which the enemy plane falls short of the collision-point isclosely related quantitatively to the over-reach of the bomb, as in thehead-on approach; this is what guarantees the hit.

The foregoing complication is the only one that arises in theapplication of the bombing method in accordance with this invention tothe general problemof approaching the target plane from any angle. Sucherror of course does not exist if the velocity component imparted to thebomb at release is. vertically upward instead. of perpendicular totheplanescollision course. Such an error could of course be eliminatedby introducing a computing sight mechanism. However, 'one of theoutstanding advantages of this method of bombing is the elimination ofsuch complex devices. The following solution is therefore suggestedwhich is based on the premise that plane-to-plane bombing attacks willbe made against formations of enemy planes as generally will be thecase. approaching on a steep diving course and desiring to detonate hisbomb in the vicinity of the leading plane of a V-formation, which pointoffers the most possibility of damage toall of the planes, instead ofaiming to hit the leading plane, the attacking plane takes thelast planeon the nearest side to him as the target (Fig. 7). Dis-. regarding allthe rest of the formation, he keeps this one flank plane in the constantorientation which establishes converging courses toward thecollision-point. This procedure, due to the deviation discussed above,will then cause the bomb to reach the vicinity of the leading plane.

Thus far the proper operation of the delayed release mechanism has beenassumed. Analysis of the mathematical factors covering this operationwill now be presented. V

Such analysis will be based upon the simplified concept of the method ofbombing wherein the attacking plane flying its collision course isconsidered a fixed reference point. It should be remembered inconnection with the following analysis, that when the attacking plane isflying an angular course with respect to the gravity axis, then theanalysis is absolutely correct only if a resultant vertically upwardtoss is imparted to the bomb thru the comattacking plane until aresultant component of velocity v' directed vertically upward has beenattained. In level flight approach, such velocity component v will beper-,

k=the number of gs of total vertical acceleration, as-

sumed to'be uniform between points A and B;

t =the time in seconds that the bomb is released after initiation of thepull-up.

Let I a v=-the vertical componentof velocity of the bomb at the instantof its release at point B.

Under such circumstances the attacking plane' H +L=the total distance ofthe fall from the apex of the trajectory back to the level of theoriginal line of flight.

If the total acceleration is kg, the net upward acceleration is g(k1).Hence oand Analysis can now be made of the proper release delay time l'pwhich will accomplish the delivery of the bomb to a point D on theprojection of the original line of flight at a time T1 seconds after thestart of the pull-up.

The above derived Equation 26 is an accurate expression for thefunctioning of the integrator. The physical significance of theexpression is that an integrator which is pre-set to deliver the bomb atthe collision point at the projection of the original line of flight ofthe plane at T1 seconds after initiation of pull-up by the attackingplane, must delay the release of the bomb by a time t which isdetermined by the rate of acceleration k at which the pull-up isaccomplished, -in accordance with the above derived equation. Therelationship between i and k is obviously a non-linear function andsimple means whereby the integrator could react to various values of kexactly in accordance with the above equations are not immediatelyobvious. However, an examination of the function k+k /1-l/k disclosesthat it develops into a very flat, practically linear curve for valuesof k above 1.5. Since the criteria could be readily established thatevery attacking plane should pull-up with an acceleration greater than1.5g (and as a practical manner the values of k will more likely begreater than 2) the behavior of the above k-function for values of kbelow 1.5 is of little interest or concern. It is therefore possible toselect a linear function of k which so closely approximates the abovederived k function that the error is negligible be- 14 tween values of kgreater than 1.5 and less than 4. Such linear function has been found tobe 2.035 (k.322.). Thus the relationship between t for k for a. fixedvalue of T1 becomes the following:

It will be noted that the analysis heretofore was based on an assumeduniform constant acceleration during pull-up of some value greater than1.5g. As a practical matter the acceleration builds up from one g to thefinal value over a finite period of time. The error caused by\such'gradual build-up over the whole period amounts to less thantwo-tenths of :a second with the above equation. This error is fullycompensated if the equation is modified as follows:

Obviously other compromise adjustments are possible involving modifyingthe co-efficient 2.035 as well as the value .322 until the combinationwhich best fits the usual flight conditions of an attacking plane isobtained.

The analysis heretofore developed demonstrates clearly that the onlyfactor which need be determined by the pilot of the attacking plane isthe time remaining before he will collide with the target, so that hemay initiate his deviation from the collision course at exactly the timeT1 for which integrating delay release mechanism is set. Having begunhis build-up or pull-out as the case may be, at the proper time T1, theintegrating delayed release mechanism will accomplish the release of thebomb at a proper velocity v determined by the rate of pull-up k. A pilottherefore does not need to know how big the enemy plane is, how fast itis flying, or its exact range at any given instant. He needs to knowonly the time to target.

The time to target may be determined by any of several known methods.Indicator means 35 carried by the airplane 31, Fig. 10, for determiningthe time-to-target comprises radar equipment, for example, which willyield instantaneous determination of range and hence rate of change ofrange. A simple division of the range at any instant by the rate ofchange of range which will generally be quite uniform will yield thetime to target. Alternatively, and for utmost simplicity ofinstrumentation, the reversing clock technique may be utilized. Inaccordance with this technique, the pilot views the approaching targetthru a sight having a target mil-scale or possibly a pair of concentricsighting circles. A clock is started when the approaching targetsubtends a certain angle determined by the scale on the sight or by thetarget filling the smaller one of the sighting rings. When the target isone-half as far away, the angle then subtended is readily determinableby application of trigonometry and may be indicated on the mil-scale ofthe sight or by the point at which the view of the target fills thelarger sighting circle. At this point the clock is reversed and startsrunning backward. The clock is then measuring time to target and willread zero at the instant of collision if the attacking planes course ismaintained. When the clock reads the value T1, for which the integratingrelease mechanism is set, the pilot energizes the integrating releasemechanism :and begins to pull-up with a uniform acceleration kg of atleast 2g. Release of the bomb is accomplished by the integrating releasemechanism when the bomb has attained a proper vertical componentvelocity v in accordance with the relationship between v and kheretofore derived.

Fig. 9 illustrates a simple form of integrating delayed, releasemechanism which will function in accordance with. Equation 28 heretoforederived, namely,

the airplane.

The mechanismcomprises a disk driven at a constant speed about ahorizontal axis by any suitable means (not shown). Preferably the speedof such drivingis adjustable Which has the effect of permitting avariation in the values of T1 of Equation 28. The disk 10 drives asecond disk 20 which is rotatably supported with its axis vertical andhence perpendicular to the driving disk 10. The disk 20 is driven byfriction by disk 10 but will of course only receive a driving force whenit is displaced from the center of driving disk 10. The disk 20 isnormally supported in a frame 21 which is in turn secured to a weight26. The weight 26 is suspended from a fixed support 24 by a spring 23.Inertia means, such as Weight 26, is guided along thepath perpendicularto the nose-to-tail center line of A stop 25 is provided to preventupward movement of weight 26 at accelerations less than one'g. Thearrangement is such that when the airplane is in level flight, the disk20 is supported atthe center of driving disk 10 and hence is not rotatedby driving disk 10. An upward acceleration of the plane will impart avertically downward force to weight 26, which during the existence ofsuch acceleration will assume a lower position determined by thecharacteristics of spring 23. The extension of spring 23, has the effectof moving the disk 20 radially from the center of driving disk 10. Hencedisk 20 is now rotated by driving disk 10 at a rate depending upon thedeflection of spring 23 and hence upon the upward accel eration producedby the plane. The disk 20 thereby rotates a suitable shaft 22 which isconnected thru gearing mechanism represented by 27 to a conventionalbomb release mechanism 33, diagrammatically shown in Fig.

10 in such a manner that a fixed extent of rotation of the shaft 22accomplishes the release of the bomb. Ob-

' viously the time required for the shaft 22 to accomplish such fixedextent of rotation depends directly upon the radial position of the disk20 with respect to the center of driving disk 10. Thus under levelflight conditions, or with a force of one g operative upon the weight26, there is no rotation of disk 20. During upward acceleration of theplane the disk 20 is rotated at a speed proportional to (a g), where ais the acceleration of the plane, and the time required for the shaft 22to complete the fixed number of revolutions is thus inverselyproportional to the acceleration. By suitable selection of the mass ofweight 26, the proportions of spring 23, and the speed of driving disk10, this mechanism will readily produce a delay release time inaccordance with the relation It will therefore be apparent that thisinvention provides. a simple yet extremely accurate method of bombing ofany type target requiring only the determination by simpleinstrumentation of time to target. The integrating delayed releasemechanism performs all necessary calculations and accomplishes releaseof the bomb with proper velocity to reach the theoretical collisionpoint with the target at the same instant that the target arrives atsuch point. Furthermore, I have provided a simple and yet rugged form ofintegrating delayed release mechanism which will. accomplish thenecessary functions required by the bombing method with a high degree ofaccuracy over the entire range of flying conditions which would be mostpractical for the application of the bombing method of this invention. VI claim:

l. The combination for bombing at target by airplane,

' upward velocity component at a fixed time to target, a

bomb, a bomb release mechanismon said airplane detachably carrying saidbomb, acceleration integratin 3. 1'5 means so oriented in said airplaneas to be responsive to vertical accelerations ,of the airplane, saidintegrating means being operatively coupled to said bombreleasemechanismand adapted to actuateisaid' mechanism in re-:

sponse to a predetermined attained vertical component of:

velocity, said predetermined velocity component being proportioned tothe said fixed time to target.

2. In a toss-bombing combination, a releasable missile,

a controllable carrier carrying said releasable missile on asubstantially collision course on a line of flight to a target,

said carrier being capable of executing an excursive' maneuver at apredetermined time before the collision to impart a'v elocity componentto the missile perpendicular to the original line of flight,'anacceleration integrator for integrating changes in said,peipendicular 'velocity component, and means responsive to said.intemechanism on said airplane detachably carrying said bomb, and anacceleration integrating means responsive to changes in said verticallyupward velocity component, operatively coupled to said bomb releasemechanism for releasing said bomb from the airplane when a predeterminedvertically upward velocity 'is attained by the airplane, saidintegrating means being so constructed and arranged as to operate saidbomb release mechanism in response to attainment of saidpredeterminedvertica component of velocity.

4. The combination for bombing a target by airplane flying a collisioncourse with respect to the target, comprising an airplane, a bombcarried by the airplane, a

bomb release mechanism, means for determining the time T1 k+k 1l/k WhereT1 is said time'remaining before collision and where k is saidpredetermined constant.

5. In the art-of toss bombing, the combination of an airplane, a missiledetachably carried by said airplane, a release mechanism for droppingsaid missile, an accelera tion responsive inertia means mounted in'andresponsive to changes of altitude of said airplane, means forintegrating changes in vertical acceleration coupled to said inertiameans, said integrating'means being coupled to the release mechanism andbeing adapted to operate the release mechanism upon and only uponattainment by said-airplane of a predetermined component of upwardvelocity.

References Cited in the file of this patent UNITED STATES PATENTS1,216,382 Wenyon -1 Feb. 2, 1917 1,433,596 Binfield Oct. 31, 19221,728,904 Herr Sept; 17, 1929 1,823,044 Holmberg Sept. 15; 19312,266,449 Ullich et :al Dec. 16, 1941 2,309,686 Winters Feb. 2, 1943.2,410,097 Morgenthaler et al. Oct. 29, 1946 (FOREIGN PATENTS I V 1801,194 France May 16, '1936,

